Some sound reproduction systems are based on so-called differential sound reproduction approaches. Due to differential sound reproduction a directivity pattern may be reproduced. Directivity patterns are known from directive microphones. Directive microphones are usually implemented by means of measuring a sound pressure gradient or an approximation thereof, as described e.g. in the publications of G. Bore and S. Peus having the title “Mikrophone: Arbeitsweise and Ausfuhrungsbeispiele” and of H. Olson having the title “Gradient microphones”. For example, a first order gradient has a figure-of-eight directivity pattern. By delaying one channel, when measuring a sound pressure difference, one can achieve directivity patterns such as cardioid or tailed cardioids. First order differential or gradient microphones are the standard in directive microphones.
Used less frequently, the same concept can also be applied to loudspeakers, as can be seen by the publication of H. Olson having the title “Gradient loudspeakers”. Though, the dimensions are about an order of magnitude larger, giving rise to different properties/limitations.
Such concepts for differential loudspeaker arrays have, when compared to conventional delay-and-sum-beamformers, the advantages of a need for only a few loudspeakers, in contrast to delay-and-sum-arrays usually featuring many loudspeakers. Furthermore, with a smaller aperture than a delay-and-sum-beamformer, the same directivity can be achieved at low frequencies.
The Patent Application WO 2011/161567 A1 discloses a dipole related processing for a loudspeaker arrangement comprising three or more transducers. In the described three driver setup, the two outermost drivers are driven in a dipole configuration (unsteered). The driver in between those two is used to produce a notch that may be steered towards the listening position. This is achieved by a (frequency selective) relative offset of the second driver signal. Here, equally spaced drivers (i.e. the distance from the first to the second driver is equal to a distance from a second to a third driver) may be used. The signal that is generated for the middle driver can have a phase difference and a (frequency selective) gain relative to the dipole configuration.
The U.S. Pat. No. 5,870,484 discloses a sound reproduction system that uses gradient loudspeakers. This publication describes in detail how dipole systems can be created, e.g. using either two or three loudspeakers, or one loudspeaker and a passive opening to achieve the dipole effect. Here, the usage of a first order gradient directivity characteristic is beneficial. The background thereof is that according to the publication a higher order gradient loudspeaker tends to be less efficient, may use a large number of transducers, more signal processing, and additional channels of amplification, as compared to first order gradient systems.
It has been found out that differential loudspeaker arrays do not have a decreasing directivity as frequency decreases, as do delay-and-sum-beamformers, their level decreases to zero as the frequency goes to zero. Furthermore, first order differential arrays are limited in directivity, to, for example, about 6 dB. Therefore, there is a need for an improved approach.